3342
J. Phys. Chem. B 2004, 108, 3342-3357
Mechanochemical Coupling in Myosin: A Theoretical Analysis with Molecular Dynamics
and Combined QM/MM Reaction Path Calculations
Guohui Li and Qiang Cui*
Department of Chemistry and Theoretical Chemistry Institute, UniVersity of Wisconsin, Madison,
1101 UniVersity AVenue, Madison, Wisconsin 53706
ReceiVed: October 20, 2003; In Final Form: January 6, 2004
To elucidate the detailed mechanism of ATP hydrolysis in myosin, molecular dynamics employing classical
force field and reaction path analyses employing a combined quantum mechanical and molecular mechanical
(QM/MM) potential were carried out. Although the QM/MM reaction path analyses have limited accuracy
due to the lack of extensive conformational sampling, the present work showed that sensible energetics much
closer to experimental measurements than previous computational studies can be obtained once the protein
environment is included. In the two associative mechanisms studied here, the pathway that involves the
conserved residue, Ser 236, as the proton relay group was found to have a lower rate-limiting barrier. However,
it was also shown that if O2γ gets protonated, the mechanism without invoking any proton relay has only a
slightly higher barrier and therefore may also contribute, especially in mutants such as Ser 236A. By performing
calculations for two different motor domain conformations, it was shown that the mechanochemical coupling
in myosin is mainly regulated by several residues in the switch I and switch II regions, such as Arg 238, Gly
457, and Glu 459. In particular, when the salt bridge between Arg 238 and Glu 459 is broken as in the
prehydrolysis conformation of the motor domain, ATP hydrolysis is highly unfavorable energetically. In this
conformation, Arg 238 is closer to ATP and therefore stabilizes the ATP state over the hydrolysis products.
Moreover, without the salt bridge, the water structure in the active site is no longer stabilized to favor the
in-line nucleophilic attack of the γ-phosphate. The results from the current work have general implications
to other molecular motors that involve ATP hydrolysis, such as kinesin, F1-ATPase and Ca2+-ATPase,
although more robust conclusions concerning the hydrolysis mechanism require more elaborate simulations
that consider protein fluctuations and other possible protonation states of ATP and the hydrolysis products.
I. Introduction
Adenosine triphosphate (ATP) is commonly referred to as
the fuel of life because its hydrolysis reaction is coupled to many
processes in living systems that require energy input.1 Important
examples include the functional cycles of motor proteins, such
as myosin,2 kinesin,3 and Ca2+-ATPase,4 which involve large
scale conformational transitions upon ATP binding and/or
hydrolysis. Therefore, it is of fundamental importance to reveal
the mechanistic details of ATP hydrolysis in these systems and
to understand how hydrolysis energetics are regulated by the
conformation of the protein;5,6 the coordination between ATP
hydrolysis and conformational properties of the protein (i.e.,
mechanochemical coupling) is the key element for energy
transductions in molecular motors.7,8 Despite previous efforts,
a mechanism with atomic details for such a fundamental reaction
in the context of important biomolecular systems is still not
available, and many proposals have been put forward (see
below). In the current work, we employ both classical molecular
dynamics9 and combined quantum mechanical and molecular
mechanical (QM/MM)10-14 calculations to explore the mechanism of ATP hydrolysis in myosin-II. The results are expected
to have important general implications to similar hydrolysis
reactions in other proteins that involve ATP hydrolysis. These
calculations are complemented with an analysis of the relative
binding affinity of ATP and ADP + Pi to myosin using an
alchemy free energy perturbation approach, which will be
reported separately. These energetics-oriented studies explore
different aspects of motor protein functions compared to
previous work based on normal-mode analysis, which focused
on the connection between conformational flexibilities of those
systems (myosin-II,15 Ca2+-ATPase,15,16 and F1-ATPase17) and
their functions.
Myosin-II (thereafter will be referred to as myosin) is one of
the best-characterized molecular motors,2,18-20 and has been the
subject of diverse types of experimental studies for several
decades. The functional cycle of the actin-myosin system has
been established in an outline form, which is commonly known
as the Lymn-Taylor model21 or the Bagshaw-Trentham
scheme.22 As shown in Scheme 1, ATP binding induces the
dissociation of myosin from the actin. Following a conformational change in the motor domain, ATP hydrolysis occurs with
a nearly unity equilibrium constant (K < 10).22 Subsequently,
the motor domain reattaches the actin polymer at the next site,
which induces the release of the hydrolysis products: inorganic
phosphate and ADP. A conformational change (“power stroke”)
of myosin occurs during or after the release of ADP, which
brings the myosin-actin system back to the rigor state. A large
body of crystallographic,23-29 electron microscopy,30,31 mutagenesis,32-35 and single molecule spectroscopy36-39 studies
have provided information with variable details into the
structures of various intermediates and residues that make
important contributions to the ATP hydrolysis. The remaining
mysteries largely concern the binding interface between myosin
10.1021/jp0371783 CCC: $27.50 © 2004 American Chemical Society
Published on Web 02/17/2004
Mechanochemical Coupling in Myosin
J. Phys. Chem. B, Vol. 108, No. 10, 2004 3343
SCHEME 1. Functional Cycle of Myosin-II-Actina
a
Only a myosin monomer is shown.
and actin, and the detailed mechanism through which actin
induces the release of inorganic phosphate and ADP.19,25
Concerning the ATP hydrolysis step in myosin, most
information has come from high-resolution structures (<2 Å)
of Dictyostelium discoideum myosin with different ligands and
kinetic analysis of various mutants.23,32-35,40 The motor domain
is believed to adopt at least two different conformations:19 the
open state and the closed state, which was proposed to favor
nucleotide binding and hydrolysis, respectively. The two active
site differ mainly in a linker region that is structurally equivalent
to the switch II region of G-proteins such as Ras p21,41 and a
key difference is the formation of a critical salt bridge between
Arg238 and Glu459 in the closed form (Figure 1; see below).
[The residue numbers in the D. discoideum myosin-II has been
used throughout the manuscript.] The open state is observed
when the active site is empty or bound with Mg‚ATP,40 Mg‚
ATP analogues (e.g., Mg‚ATPγS and Mg‚AMP‚PNP),42 and
Mg‚ADP.42 The closed-state is observed with the active site
occupied by ATP hydrolysis transition state analogues: Mg‚
ADP‚AlF4- 43 and Mg‚ADP‚VO4.44 With Mg‚ADP‚BeF3, both
Figure 1. Difference between the prehydrolysis (1FMW) and hydrolyzing (1VOM) state of the D. discoideum myosin-II motor domain. (a)
Superposition of the motor domain in the two states based on the backbone atoms in residue 1-650: red and blue corresponding to 1FMW; green
and yellow indicating the 1VOM state. As illustrated by the arrow, the majority of the conformational difference occurs in the C terminal converter
region. (b) Structural difference between the active sites of the two states, with the same color coding. The ATP molecule is shown in van der
Waals representation, and the three important motifs in ATP hydrolysis are shown in ribbon. Evidently, the major changes are associated with the
relative arrangements of the switch I and switch II regions, in particular the salt bridge between Arg 238 and Glu 459.
3344 J. Phys. Chem. B, Vol. 108, No. 10, 2004
Li and Cui
SCHEME 2. Two Associative Mechanisms for ATP Hydrolysis in Myosina
a
In path B, a route in which the water proton is transferred directly to O3γ instead of O2γ has also been studied (path B1).
closed19,45 and open43 forms have been observed in X-ray crystal
structures, which highlights the subtle nature of factors that
control the transition between the two conformational states and
the intrinsic structural flexibility of the motor domain.15
Moreover, these structures clearly indicate that ATP binding
alone is not sufficient to stabilize the motor domain to the
conformation appropriate for hydrolysis. Since no catalytic base
in the form of amino acid side chains is found within 5.5 Å of
the beryllium or vanadium that mimic the γ-phosphate, it is
natural to conclude that water molecule(s) in the active site is
the nucleophile and the γ-phosphate serves as the general base
for its own hydrolysis. A highly conserved active site Ser residue
(Ser 236) was proposed to serve as a relay in this process,
making the proton transfer proceed with the better stereochemistry (Scheme 2).43,44 Although such a proton-relay mechanism
has been discussed in model calculations for the dissociatiVe
mechanism of phosphate hydrolysis in solution,46,47 it has not
been firmly established in either the context of hydrolysis in
enzymes or associatiVe mechanism of phosphate hydrolysis. As
a matter of fact, mutation experiments found that the S236A
mutant has rather normal hydrolysis activity.33,35 Alternative
mechanisms that employs Lys 185 as the general acid that
protonates the γ-phosphate of ATP has also been proposed based
on recent Car-Parrinello (CP) simulations,48 although the
observation that led to this mechanism might be an artifact due
to the small size of the model used in the calculations.14 Another
pair of residues that were found to be essential to hydrolysis
involves Arg 238 and Glu 459, which form a salt bridge in the
closed form (Figure 1b).44 Mutation involving either one of these
residues significantly impairs the hydrolysis efficiency (e.g.,
E459V hardly affects ATP binding, but reduces ATP hydrolysis
by a factor of 106);49,50 a double mutation that flips the positions
of the two residues, by contrast, retained a substantial amount
of ATPase activity.49,50 These results were explained in terms
of the role of the salt bridge in maintaining the appropriate water
structure in the active site that favors hydrolysis, although a
detailed mechanism is not available; e.g., it was proposed that
the second active-site water molecule, which bridges the lytic
water and Glu 459, can serve as the general base and accept
one proton from the lytic water.50 For other residues in the
switch I and switch II regions, mutation experiments also
provided insights into their roles in ATP binding and hydrolysis.32-35,38 To better establish the nature of their contributions, however, a detailed analysis with energetics is of
significant value.
In the present work, we have carried out both classical
molecular dynamics (MD) simulations and combined quantum
mechanical and molecular mechanical (QM/MM) reaction path
calculations to analyze the mechanism of ATP hydrolysis in
myosin with a stochastic boundary condition. Classical MD
simulations were employed to investigate the structure and
dynamics of active site residues and water molecules, and how
these are affected by the conformation of the motor domain in
different kinetic states (prehydrolysis state and hydrolysis
“transition state”). The QM/MM calculations were used to
qualitatively analyze two popular associatiVe mechanisms for
the hydrolysis of ATP, the contribution from amino acids and
the dependence of hydrolysis energetics on the motor domain
conformation. Computational methods and simulation details
are described in section II, which is followed by the presentation
of results and relevant discussions in section III. We summarize
several conclusions in section IV.
II. Computational Methods
All the simulations here have been set up using the stochastic
boundary conditions (Figure 2).51-53 A water sphere of 18 Å is
centered on the active site of myosin-II motor domain, and the
system is divided into the reaction (<16 Å), buffer (16-18 Å)
and reservoir zone (>18 Å). Atoms in the reservoir zone were
excluded in the simulation, and those in the buffer zone were
subject to harmonic constraints and random force following the
Mechanochemical Coupling in Myosin
Figure 2. Stochastic boundary setup for the present simulations. The
protein atoms areshown in the ribbon format, and are color-coded
according to the type of the amino acids (white, nonpolar; green, polar;
blue, acidic; red, basic). The ATP molecule and the magnesium ion
are shown in van der Waals representations. The solvent molecules
are shown as dots.
Langevian equation. In the classical MD simulations, the
integration time step was 1 fs, and all bonds involving hydrogens
are constrained using SHAKE.54 The temperature of the system
was maintained at 300 K using the mixed molecular dynamics/
Langevian dynamics scheme unique to the stochastic boundary
simulations.51-53 All classical simulations were performed using
the CHARMM program55 with the CHARMM 22 force field56
for the protein atoms and ATP/ADP‚Pi.
In the QM/MM calculations,10-13 the QM region included
the tri-phosphate and part of the ribose group of ATP, the
catalytic water molecule(s), the Mg2+ ion and all its ligands
(Thr 186 and Ser 237 and two water molecules) as well as the
conserved Ser 236 (Figure 3). In the current work, ATP was
assumed to be fully deprotonated (i.e., -4 charge) and the
ligands of Mg2+ were assumed to remain protonated; all other
titritable groups were kept in their normal protonation states
(i.e., Lys, Arg were protonated, Asp, Glu were deprotonated),
which are consistent with a simple estimate of pKa’s using
Poisson-Boltzmann approach.57 All other atoms, including the
charged (e.g., Lys 185) and polar side chains (e.g., Asn 233) as
well as main chain groups (e.g., Gly 457) that are close to the
reacting atoms (Figure 3), were treated with the CHARMM 22
force field;56 this makes it convenient to analyze the qualitative
contributions from protein residues to the ATP hydrolysis
energetics. A Poisson-Boltzmann (PB) charge-scaling scheme58
was introduced to account for solvent shielding in addition to
that from the explicit water molecules in the model. The
algorithm makes use of several PB calculations to determine a
set of scaling factors to reduce the partial charges of charged
side chains in the QM/MM calculations so as to avoid artifactual
structural changes.59 Link atoms were introduced to saturate the
valence of the QM boundary atoms; the link atoms interact with
the MM atoms, except the “link host” MM atom (e.g., the CR
atoms in this case), through electrostatic terms; no van der Waals
interactions are included. This scheme has been shown to be a
satisfactory way to treat the QM/MM interface, particularly
when the charges of the atom in the neighborhood of the
link atom are small, which is true in the present case.60 The
J. Phys. Chem. B, Vol. 108, No. 10, 2004 3345
Figure 3. Active site structure of the D. discoideum myosin-II motor
domain in the hydrolyzing state (PDB code 1VOM). The loops indicate
the three important structural motifs (the P-loop, switch I, and switch
II), which are commonly found in proteins involve nucleotide binding
and hydrolysis; they are color-coded as in Figure 2. Part of the ATP
molecule, the magnesium ion and several important water molecules
are shown in the CPK format, while the side chains of several important
residues are shown in the line form. Among those, the shown moiety
of ATP, the magnesium ion and its ligands (Thr 186, Ser 237, and two
water molecules), the lytic water (Wat 1) and Ser 236 were treated
with QM in the QM/MM calculations (see text).
QM method used in geometry optimization and reaction
path calculations is HF61/3-21+G,62,63 and B3LYP64-66/
6-31+G(d,p)67,68 was used in single point energy calculations;
test calculations indicate that such a scheme gave very similar
energetics compared to using B3LYP/6-31+G as the QM
method in geometry optimizations. The van der Waals parameters used for QM atoms are the standard CHARMM parameters. Benchmark calculations for phosphate hydrolysis reactions
in the vacuum and solution indicate that B3LYP/6-31+G(d,p)
energetics are sufficient for our purpose of comparing various
mechanisms.
In the reaction path calculations, an initial guess was first
generated by adiabatic mapping69 calculations employing approximate reaction coordinates, such as the antisymmetric stretch
involving the proton donor, the proton and the proton acceptor
atoms.59 This path was then further refined using the conjugate
peak refinement70 approach in CHARMM to obtain more
accurate information about the relevant saddle points. All the
protein atoms were allowed to move in the reaction path
calculations, although their thermal fluctuations are clearly not
included. Therefore, the current reaction path results should be
taken as qualitative, although previous experience suggests that
this type of calculations is capable of providing mechanistic
insights.59,71,72 Calculations employing a more realistic treatment
of protein motions and structural response to the chemical
event,14,73,74 which necessarily involves less expensive QM
methods,75-77 are in progress and will be reported in the near
future.
As to the starting atomic coordinates, two high-resolution
X-ray structures from D. discoideum were used. They were
determined with Mg‚ATP (PDB code 1FMW40) and Mg‚ADP‚
vanadate (PDB code 1VOM44) as the ligands, respectively, and
were believed to correspond to the prehydrolysis and hydrolyzing kinetic states, respectively.19,23 The starting structures for
3346 J. Phys. Chem. B, Vol. 108, No. 10, 2004
Li and Cui
Figure 4. Overlay of the averaged positions for part of ATP/ADP‚Pi and several aminoacids in the active site from 500 ps classical molecular
dynamics simulations for 1VOM. The color-coded ones are from ATP simulations, while the yellow ones are from the MD simulation in which
ATP was replaced by ADP‚Pi. Note that there are essentially no major structural changes during the 500 ps of simulations. Key distances are given
in angstroms; those with and without parentheses are for the ATP and ADP‚Pi simulations, respectively.
QM/MM calculations are the minimized X-ray structures, rather
than those from classical MD simulations; this is based on the
consideration that structures from classical MD simulations are
usually fairly different from the X-ray data, which are not
appropriate for QM/MM calculations unless free energy quantities are calculated.74 By comparing simulation results for these
two structures, we are able to explore the connection between
ATP hydrolysis and conformational properties of the motor
domain in myosin. In the 1VOM simulations, the ADP‚vanadate
was replaced by ATP or ADP‚Pi.
III. Results
In this section, we first describe the features of the myosin
active site from classical molecular dynamics simulations, and
then move on to the combined QM/MM analysis of the catalytic
and regulatory mechanism of ATP hydrolysis.
III.1. Active Site Structure and Dynamics of Myosin in
the Hydrolyzing (1VOM) and Prehydrolysis (1FMW) States.
Since MD simulations have been reported on the myosin motor
domain before,48,78 we will only describe the results briefly and
focus on the differences between the prehydrolysis (1FMW)
and hydrolyzing (1VOM) states.
With the 1VOM structure, the active site is stable in the 500
ps of MD simulations with either ATP or ADP‚Pi bound; the
same trend was also found in alchemy free energy simulations
that last for several nanoseconds (Li et al., to be submitted).
This includes not only the critical interactions between ATP
and the surrounding amino acids (Figure 4) but also the two
active-site water molecules resolved in the X-ray structure.44
As shown in Figures 4 and 5c,d, these water molecules form a
hydrogen-bonding network that connects the γ-phosphate in
ATP and Glu 459; the latter is in the switch II region and is
stabilized by a salt bridge interaction with Arg 238 in the switch
I region. Because of such a network, the water closer to the
γ-phosphate is in a favorable position for a nucleophilic attack;
as shown in Figure 5a,b, the OW-PγATP distance is stable around
3.2 Å, and the OW-PγATP-O3βATP angle undergoes only mild
fluctuations about 155°.
The active site undergoes small structural changes when the
ATP molecule was replaced by ADP‚Pi. As shown in Figure
4, the averaged structure from the two sets of MD simulations
superimpose very well, such as the positions of Lys 185, Ser
236 and Gly 457. The salt bridge between the switch I and
switch II regions also remained intact. The small structural
perturbation associated with replacing ATP by ADP‚Pi observed
here led us to believe that reaction path calculations using a
QM/MM potential is a meaningful first step to explore the
energetics and mechanism of ATP hydrolysis in myosin (section
III.2.3).
The prehydrolysis state (1FMW) has a very similar overall
structure compared to the hydrolyzing state (1VOM); the first
650 amino acids can be aligned to have only a 2.4 Å RMS
difference for the backbone atoms, while the C-terminal
converter domain undergoes a large swinging displacement
(Figure 1a).15,40 In the present study, we only focus on the active
site region, for which a key difference is the relative arrangement
of the switch I and switch II regions (Figure 1b). In 1FMW,
the salt bridge between Glu 459 and Arg 238 is broken, and
the mainchain of Gly 457 can no longer stabilize the γ-phosphate of ATP. These trends remained during the MD simulations
for 1FMW. As shown in Figure 6, Arg 238, Glu 459, and Gly
457 are among the ones with the most significantly different
average positions between 1VOM and 1FMW simulations. In
1FMW, Arg 238 is substantially closer (∼0.4 Å) to the
γ-phosphate, and Glu 459 and Gly 457 are further away from
Arg 238 and ATP, respectively. Because of these structural
changes, the water distributions in the active site are also
different in 1FMW and 1VOM. The trapped water molecules
underwent significantly larger fluctuations in 1FMW (Figure
5c,d), and orient themselves differently. As shown in Figure
5a,b for the two water molecules close to the γ-phosphate, the
Ow-PγATP distances vary from 3 Å to 4.2 Å, and the OWPγATP-O3βATP angles vary from 100 to 150°. Therefore, the
water molecules in 1FMW are not in as favorable positions as
the ones in 1VOM for nucleophilic in-line-attacks. The energetical consequences of these differences will be revealed by
the subsequent QM/MM analysis (Section III.3).
Similar to 1VOM, the active site underwent small structural
changes when the ATP was replaced by ADP‚Pi during the 500
ps of MD simulations (not shown).
Mechanochemical Coupling in Myosin
J. Phys. Chem. B, Vol. 108, No. 10, 2004 3347
Figure 5. Instantaneous values of several key geometrical parameters that characterize the water structure in the active site during MD simulations.
For both 1FMW and 1VOM simulations, the active site is occupied by ATP. The geometrical parameters include (a) the distance between the
oxygen in lytic water molecule(s) and Pγ of ATP, (b) the angle between the oxygen in lytic water molecule(s) and Pγ-O3β of ATP, (c) the
distance between the oxygen atoms in the two water molecules close to the γ-phosphate, and (d) the minimal distance between Glu 459 and the
oxygen atoms in the two water molecules close to the γ-phosphate. Note the larger fluctuations and deviation from ideal in-line attack orientations
associated with the 1FMW simulations.
Figure 6. Similar to Figure 4, but for 1FMW and 1VOM simulations with ATP as the ligand. Note the significantly differences in the switch II
region. Only the distances that are very different in the two sets of simulations are given.
III.2. Energetics and Mechaisms of ATP Hydrolysis in the
Hydrolyzing Structure (1VOM). As discussed in the Introduction, at least two possible reaction schemes have been proposed
for ATP hydrolysis in myosin (Scheme 2); one mechanism
involves a direct proton transfer from the attacking water to
the γ-phosphate (path B), and the other involves Ser 236 as the
proton relay (path A). According to the QM/MM reaction path
results summarized in Figure 7, path A has a lower rate-limiting
activation barrier and therefore is likely to be the favorable
pathway in wild-type myosin; the energetics associated with
path B depend on which γ-oxygen gets protonated, and the
lower energy route has a rate-limiting barrier only ∼4 kcal/
mol higher than path A.
In path A, the lytic water molecule first transfers one of its
proton to the hydroxyl oxygen in Ser 236, which in turn transfers
its hydroxyl proton to the γ-phosphate. Only one transition state
3348 J. Phys. Chem. B, Vol. 108, No. 10, 2004
Li and Cui
Figure 7. Schematic potential energy diagrams associated with the several hydrolysis pathways studied here with QM/MM reaction path calculations.
For the definition of path A and B, see Scheme 2.
was found for these two proton transfers. In TSA1 (Figure 8),
the water proton is shared between the donor (Ow) and the
acceptor atoms (OS236), while the hydroxyl proton in Ser 236
has nearly completed the transfer to the γ-phosphate oxygen
(O2γ). The distance between the lytic water and Pγ has decreased
from 2.852 Å in the reactant (R) to 1.916 Å in TSA1, and the
distance between Pγ and the bridging β oxygen (O3β) correspondingly has increased from 1.709 Å to 1.805 Å. In the
pentacoordinated intermediate, INTA, the Ow-Pγ distance is
further shortened to 1.794 Å and the Pγ-O3β distance is
lengthened to be 1.855 Å. To lead to the final hydrolysis
products, a rotation of the newly formed O2γ-H group has to
occur (TSA2), which induces the break of the bond between
Pγ and O3β. In the final product, PA, the O2γ-H interacts with
O3β through a very short hydrogen bond, in which the H‚‚‚O3β
is only 1.319 Å. Although this short distance could be an artifact
of the HF/3-21+G method used in geometry optimization, it is
reasonable to expect a strong interaction between the negatively
charged ADP and the OH group in Pi. Despite the stabilizing
interactions from positively charged and polar groups in the
active site, such as Mg2+, Lys 185, and the main chain of Gly
457, there is substantial repulsion between the negatively
charged ADP and Pi. As a result, the hydrolysis products are
nearly the same in energy compared to ATP (-0.4 kcal/mol,
Figure 7) in the myosin motor domain, rather than being much
more stable than ATP as reflected by the large exothermicity
associated with the hydrolysis in solution. In the entire hydrolysis process, the second transition state is the highest in energy,
which is only 3 kcal/mol higher compared to TSA1; the present
calculations are not sufficiently accurate to rule out the
possibility that TSA1 is rate-limiting. The pentacoordinated
intermediate, INTA, is only marginally stable as implied by
the small barriers that separate it from the reactant and product
states, and it is 21.2 kcal/mol higher in energy than R. The
high energy nature of the intermediate makes it in general
difficult to capture in structural studies, and the first pentavalent
intermediate in a phosphoryl transfer reaction has only been
reported very recently.79
In path B, two possible routes can be followed depending on
to which γ-oxygen is the water proton transferred (Scheme 2).
With the water geometry in R (Figure 8), the O2γ is “protected”
by the hydrogen-bonding interaction with Ser 236, and the lytic
water proton is oriented toward O3γ. In the corresponding
transition state (TSB1), the Ow-Pγ distance is longer than that
in TSA1, which are 1.996 and 1.916 Å, respectively; the
Pγ-O3β distances are 1.744 and 1.805 Å, respectively, which
are also consistent with the earlier nature for TSB1. The proton
transfer occurs in a four-membered ring arrangement, where
the Pγ-Ow-H angle is only 69.9°, which is not optimal from
a stereochemistry point of view. Indeed, the barrier associated
with TSB1 is substantially higher than TSA1 by nearly 16 kcal/
mol, although the difference does not necessarily come entirely
from the four-membered ring arrangement in TSB1. For
example, due to the interaction with the lytic water in TSB1,
O3γ loses interaction with the mainchain of Gly 457 and a water
molecule trapped in the active site, which are present in TSA1;
the relevant hydrogen bonding distances are 2.05, >3 Å in TSB1
compared to 1.73 and 1.70 Å in TSA1. The pentavalent
intermediate along path B1 (INTB) is slightly more compact
than INTA in terms of the Ow-Pγ and Pγ-O3β distances by
approximately 0.05 and 0.03 Å, respectively. Because of the
different protonation patterns of γ-oxygens, INTB is less stable
than INTA by nearly 8 kcal/mol. In addition to the differences
in the interaction between O3γ with Gly 457 and active water
as already observed in the transition states, protonation of O3γ
in INTB weakens the interaction with a charged group, Lys
185, while the protonation of O2γ in INTA weakens interactions
with neutral groups such as Ser 236 and Ser 181. The subsequent
isomerization of the O3γH group in TSB2 takes a similar amount
of energy (∼3 kcal/mol) as in path A, and the final hydrolysis
products are slightly more stable than the reactant state.
Interestingly, the final products have ADP protonated and the
Mechanochemical Coupling in Myosin
J. Phys. Chem. B, Vol. 108, No. 10, 2004 3349
Figure 8. Geometries for the reacting groups during the hydrolysis reaction following path A, when the motor domain is in the hydrolyzing state
(1VOM). The geometries were obtained from HF/3-21+G/CHARMM reaction path calculations (see section II); distances are given in angstroms,
angle and dihedral angles are given in degrees. Note that the protein environment has been included in the framework of the stochastic boundary
condition (Figure 2 and section II of main text), although only the QM atoms are shown here.
inorganic phosphate monprotonated, although the hydrogen bond
between the two is very short with a distance between the
hydrogen and the acceptor atom (O3γ) of 1.377 Å.
Alternatively, path B can proceed through a proton transfer
from the lytic water to O2 γ (path B2). To do so, however, the
reactant geometry has to change to allow the direct interaction
between the water proton and O2γ. By rearranging orientations
of the protons in the lytic water and Ser 236, we obtained
structure R′ (Figure 10). The lytic water in R′ is directly
hydrogen bonded to O2γ and Ser 236 is hydrogen bonded to
the oxygen in the lytic water with rather short hydrogen bond
distances around 1.5 Å. The distance between the lytic water
and Pγ is a bit longer, 3.261 Å, than that in R (2.852 Å), and
the angle Ow-Pγ-O3β is less linear (150.2° vs 175.7° in R). In
the corresponding transition state, TSB1′, the Ow-Pγ distance
is also longer, which is 2.250 Å compared to 1.996 Å in TSB1.
The interesting difference with TSB1 is that TSB1′ appears to
be later in nature based on the observation that the water proton
has almost completed the transfer to O2γ; the Hw-Ow and HwO2 γ distances are 1.435 and 1.043 Å, respectively. Following
3350 J. Phys. Chem. B, Vol. 108, No. 10, 2004
Li and Cui
Figure 9. Similar to Figure 8, but for the structures involved in path B1.
TSB1′, the pentavalent intermediate is essentially the same as
INTA, and therefore the rest steps have the same energetics as
discussed for path A. TSB1′ is lower than TSB1 by nearly 8
kcal/mol because it is less favorable to protonate O3γ as in the
latter, which leads to weaker interactions with the mainchain
of Gly 457 and an active site water molecule. Nevertheless,
TSB1′ is still higher than TSA2 by ∼5 kcal/mol, which is about
the uncertainty of the present QM/MM reaction path analysis.
Therefore, although path A is likely to be the dominant path in
wild-type myosin, we cannot exclude the possibility that path
B2 also contributes (see below).
To further understand qualitative contributions from various
residues, perturbation analysis59,72,80 has been carried out on
critical QM/MM energetics. For path A, it is seen that the same
cluster of residues contribute to different steps of the hydrolysis,
such as Ser 181, Lys 185, Asn 233, Arg 238, and Glu 459;
several Gly residues also contribute significantly due to their
main chain interactions. The sign of their contributions, however,
change depending on the nature of the reaction steps. Take Lys
185, for example, it favors the formation of INTA and the final
product P over the reactant state by more than 6 kcal/mol, while
it contributes unfavorably to the barrier TSA2 (Figure 11).
Apparently, as O2γ gets protonated in INTA and P, the negative
charge distribution is more shifted toward O3γ, which results
in a stronger interaction with Lys 185. The critical role of Lys
185 is consistent with the previous mutation study, which
showed that the Lys185Q mutation abolished the ATPase
activity.33 A neutral residue, Ser 181, which interacts with O2γ
in the reactant state (Figure 1), significantly destabilize INTA
and PA over R due to the protonation of O2γ in the former two
states. The fact that Ser 181 is not required for catalysis is
qualitatively consistent with the mutation result that Ser181A/
Ser181T showed nearly normal ATPase activity.33 Two glycine
residues in the P-loop region, Gly 182 and Gly 184, were found
to contribute favorably (∼2 kcal/mol) to TSA1 and INTA, while
Gly 457 in the switch II region significantly favored the
formation of the hydrolysis product by ∼3 kcal/mol. The
contribution from Gly 457 is consistent with the previous
mutagenesis result that mutating Gly 457 into Ala reduced the
hydrolysis activity by ∼105 fold.32,34 For the two Asn residues
in the active site, Asn 233 and Asn 235, their contributions were
found to be small for the rate-limiting step in path A (Figure
11). This observation is consistent with the experimental data
that Asn235A and Asn235I had near-normal ATPase activity;33,35 Asn233 was believed to be more important for ATP
binding because Asn233A did not bind ATP.33,35 Since the
perturbation analysis was made with a limited number of
configurations from QM/MM reaction path calculations, we
Mechanochemical Coupling in Myosin
Figure 10. Similar to Figure 8, but for the structures involved in path
B2.
J. Phys. Chem. B, Vol. 108, No. 10, 2004 3351
emphasize that the results should be taken as approximate,
especially for those have small values (<2 kcal/mol). For
example, the perturbation results indicate that D454 and S456
make small unfavorable contributions to the hydrolysis intermediate and product formations (Figure 11); experimentally,
S456A and S456L mutants showed nearly the same ATPase
activity as the wild type,34,38while mutating D454 into Ala
decreased the hydrolysis rate by ∼2000-fold.32 More conformational sampling and calculations with the actual mutations
need to be performed in the future for a better understanding
of contributions from these residues.
Since the major difference between path A and B is in the
first transition state, only the perturbation results for R(R′) f
TSB1 (TSB1′) are shown in Figure 12. Because O3γ and O2γ
are protonated in TSB1 and TSB1′, respectively, it is expected
that Ser 181 disfavors TSB1′ while it has a negligible effect on
TSB1, which were confirmed by the perturbation analysis
(Figure 12). For the similar reason, we expect that Lys 185 has
different effects on the two routes of path B. Interestingly, the
contribution from Lys 185 was found to be rather small in the
transition states, although the expected effect did show up clearly
in the intermediates (not shown). This indicates that charge
redistribution among the γ-oxygen atoms has not yet occurred
in the transition states, and the weaker interactions between O3γ
and mainchain of Gly 457 and the active site water in TSB1
are the major causes for the higher barrier compared to TSB1′.
In TSB1, we note that Glu 459 contributes favorably to the
barrier with a magnitude larger than that in TSA, while Asn
233 contributes unfavorably due to the weakened interaction
with O2γ. Overall, the perturbation analysis did not indicate any
extra destabilizing effect from the protein that significantly
disfavors path B2 over path A. Therefore, the different barrier
heights associated with the two mechanisms are mainly determined by the “intrinsic” nature of the direct proton transfer (path
B2) vs relayed proton transfer (path A).
Figure 11. Results from perturbation analysis of the QM/MM energetics associated with selected steps in path A. Positive (negative) values
indicate favorable (unfavorable) contributions.
3352 J. Phys. Chem. B, Vol. 108, No. 10, 2004
Figure 12. 12. Similar to Figure 11, but for the initial transition states
in path B1 and B2.
III.3. Energetics of ATP Hydrolysis in the Prehydrolysis
Structure (1FMW). With the 1FMW structure of the motor
domain, QM/MM minimizations led to structures like R_FMW
in Figure 13. Similar to the trend found in classical MD
simulations discussed above, the difference in the active site of
1FMW led to different water positions. In R_FMW, which is
one of the representative reactant state structures, the water
molecule nearby the γ-phosphate is far from the ideal in-line
attack orientation; several other QM/MM minimizations with
different initial geometries also led to the similar arrangement.
The Ow-Pγ distance is 4.021 Å, and the Ow-Pγ-O3β angle is
118.1°, which can be compared to the values of 2.852 (3.261)
Å and 175.7° (150.2°) in R (R′). The lytic water is no longer
in close contact with Ser 236, and therefore the only possible
mechanism to follow is path B. In TSB_FMW, the key
geometrical parameters of reacting species are quite similar to
those in TSB1, such as the Ow-Pγ distance and the fourmembered ring motif (Figure 13, 9); the same trend holds for
the pentacoordinated intermediate and the final product. For
example, in P_FMW, the ADP is also protonated and the
inorganic phosphate is monoprotonated, as in PB. The energetics, however, are very different in the two cases. In 1FMW,
the first barrier is 53.6 kcal/mol above R_FMW, which is nearly
15 kcal/mol above even the higher barrier (TSB1) in the path
B of 1VOM; the intermediate in 1FMW is also very high in
energy, 45.4 kcal/mol, and the hydrolysis products are 17.3 kcal/
mol higher than the reactant state R_FMW.
By comparing results from perturbation analysis for 1FMW
(Figure 14) and 1VOM (Figures 11-12), one can see that the
two residues that stand out as destabilizing TS1_FMW and
P_FMW are Arg 238 and Ser 456, which are in the switch I
and switch II regions, respectively (Figure 1). Apparently, these
two residues interact more favorably with the ATP state than
with other chemical states, and their contributions are more
distinct in 1FMW because they are closer to ATP in 1FMW
than in the 1VOM structure (Figure 3). In addition, the favorable
Li and Cui
interaction from the mainchain of another switch II residue, Gly
457, is absent in 1FMW because Gly 457 is far from the
γ-phosphate (Figure 4). Nevertheless, the difference in the direct
protein contributions between the two sets of structures is
smaller than the difference in the calculated energetics. For
example, the sum of significant unfavorable contributions
(absolute value >1 kcal/mol) to the hydrolysis exothermicity
is ∼28 and 25 kcal/mol for 1FMW and 1VOM, respectively,
while that for favorable contributions is ∼18 and ∼20 kcal/
mol, respectively; these differences are smaller than the
computed difference in hydrolysis exothermicity of ∼17 kcal/
mol. Although considering the highly qualitative nature of the
perturbation analysis, this observation suggests that an essential
part of the conformational dependence of hydrolysis energetics
has to come from the orientation of water molecules in the
reactant state, which in turn is controlled by the protein structural
feature in the active site, such as the salt bridge between the
switch I and switch II regions (Arg 238-Glu 459).
III. 4. Discussions: Catalytic and Regulation Mechanisms
of ATP Hydrolysis in Myosin. ATP hydrolysis is a key reaction
in bioenergetics, and regulation of the hydrolysis reaction by
protein conformations is the key element of the mechanochemical coupling. Providing atomic details about the catalysis and
regulation of ATP hydrolysis is the major challenge in understanding energy transductions in biological systems. In the
present work, we have made the first step toward this goal with
classical molecular dynamics and combined QM/MM reaction
path calculations for myosin-II.
On the ATP hydrolysis mechanism, two possible associatiVe
mechanisms have been studied (Scheme 2). Both involve an
active site water molecule as the nucleophile and the phosphate
itself as the general base; the two mechanisms differ in the way
that the water proton gets transferred to the γ-phosphate. It was
found that the energetics of path B, which involves a direct
proton transfer from the lytic water to the γ-phosphate, depend
on whether O2γ or O3γ is the proton acceptor. The route that
protonates O2γ (path B2) is lower in energy, because the
mainchain of Gly 457 and an active site water can further
stabilize O3γ as the charge on the γ-phosphate reorganizes during
the proton transfer; Lys 185 also plays a role although the effect
was found to be small at the transition state and more notable
in the intermediate. Nevertheless, both routes in path B have
barriers higher than that in path A, where Ser 236, a conserved
residue, serves as the proton relay group. Perturbation analysis
indicated that protein residues do not have particularly destabilizing effects in path B2, and therefore, the difference between
path A and B is largely due to the stereochemical factors intrinsic
to direct proton transfers and OH relayed proton transfers. It
has been demonstrated in previous studies46,47 that a relayed
proton transfer is energetically more favorable than a direct
proton transfer because the latter involves a four-membered ring
transition state (i.e., similar to TSB1 in Figure 9) in which it is
difficult to maximize orbital overlaps between the proton, donor
and acceptor atoms simultaneously. In relayed proton transfers,
by contrast, both proton transfers can proceed with nearly linear
arrangements of the protons, the donor and acceptor atoms (i.e.,
similar to TSA1 in Figure 8), which lead to lower barriers.
Although these previous calculations have emphasized the
participation of extra water molecules in dissociatiVe pathways
of phosphate hydrolysis, we expect that the similar stereochemical argument to hold for associative mechanism as well;
whether the process is fully concerted or stepwise81 is not the
essence of the problem. A major argument against the proton
relay mechanism is that the organization of water molecules
Mechanochemical Coupling in Myosin
J. Phys. Chem. B, Vol. 108, No. 10, 2004 3353
Figure 13. 13. Similar to Figure 8, but for path B1 when the motor domain is in the prehydrolysis state (1FMW).
into the specific orientation appropriate for proton relay is
associated with a substantial amount of entropic penalty.81
Although this is clearly true in solution (Cui et al., work in
progress), we note that Ser236 is already well positioned to act
as the relay group and therefore the relay mechanism is not
expected to suffer from any significant entropic penalty in the
myosin active site; more quantitative assessments require further
calculations that include the fluctuations of the protein environment. We note that a recent QM/MM analysis of ATP hydrolysis
in F1-ATPase82 found a similar trend as in the current study.
That is, a two-water associative mechanism is energetically
much more favorable than the single-water pathway, although
different active site water molecules were used as the nucleophile in the comparison (we note that the energetics calculated
in ref 82 are very endothermic, which is not consistent with
the measured equilibrium constant of one22 or the free energy
perturbation calculations of Yang et al.83 using a classical force
field; the reason behind the discrepancy is not entirely clear,
although one factor is that different X-ray structures were used
in ref 82 and 83). In contrast to that study, however, the
difference between path A and path B2 in myosin was found
to be rather small (∼4 kcal/mol compared to ∼20 kcal/mol
difference found in ref 82), especially considering the uncertainty associated with the present reaction path calculations.
Therefore, we do not expect a spectacular change in the
hydrolysis activity if Ser 236 is mutated to a residue that is
incapable of relaying proton transfers. This is indeed the result
of mutagenesis studies, which showed that Ser236A has rather
normal hydrolysis activity.33,35 Therefore, the fact that Ser 236
is conserved can be explained by the argument that it plays a
significant role for the binding of ATP. Alternatively, it is
possible that the Ser236A mutation introduces extra water
molecules into the active site as the proton relay group; clearly,
a high-resolution X-ray structure for the S236A mutant would
be very useful to further clarify the role of Ser 236.
The calculated energetics for the slightly favored path A are
only in fair agreements with experimental measurements, which
is expected for a QM/MM reaction path analysis without
including the thermal fluctuation of the protein environment.
The hydrolysis products are nearly iso-energetic as the reactant
state. This is consistent with the experimental observation that
the equilibrium constant is nearly unity for the hydrolysis
(K < 10),19,22 which is sensible from energy transduction point
of view (see below). The small equilibrium constant is also
3354 J. Phys. Chem. B, Vol. 108, No. 10, 2004
Figure 14. 14. Similar to Figure 11, but for path B1 when the motor
domain is in the prehydrolysis state (1FMW).
consistent with the 18O exchange experiments which showed
rapid reversal of the hydrolysis.84,85 The barriers calculated here
are unfortunately substantially higher than experimental measurements; the calculated rate-limiting barrier for path A without
zero-point corrections is 25.9 kcal/mol. Even if taking 2-3 kcal/
mol zero-point correction into account, which is typical for
proton-transfer reactions,59 the barriers are still above 20 kcal/
mol. Experimental measurements gave ATPase rate constants
that range from 1 to 100 s-1,22,38 which corresponds to free
energy barriers in the range of 15-17 kcal/mol (converted based
on transition state theory and a prefactor of kT/h at room
temperature). The discrepancy between the calculations and
experimental barrier cannot be clearly resolved here, and we
will defer a more quantitative study using a more efficient QM/
MM approach to the future. However, what is clear from the
current study is that neither path A or path B2 has unreasonable
energetics compared to experimental measurements. We note
that our results are much closer to experimental measurements
than any previous theoretical studies of myosin. For example,
Okimoto et al.78 calculated a barrier of 42 kcal/mol using a small
active site model in the gas-phase based on a mechanism similar
to path B. It was suggested that the high barrier is due to the
neglect of the second active site water molecule,50 but we
suspect that the neglect of the protein environment in that study
was the major limitation.
The roles of amino acids in the active site, in particular those
in the switch I, switch II, and the P-loop region, have been
analyzed with perturbation analysis. Although these analyses
have been carried out for a limited configurations from reaction
path calculations and thus are highly approximate, the results
are qualitatively consistent with experiments including Lys
185,33 Ser 181,33 Asn 233,35 Asn 235,33,35 and Gly 45732,34
(Figure 11). For Asp 45432 and Ser 456,34,38 more conformational sampling and actual mutant calculations have to be
performed in the future to better understand their contributions.
Li and Cui
In the elegant experiments of Hackney et al.,86 it was found
that although γ-oxygen atoms could undergo rapid exchange
with the solvent, the bridging β-oxygen does not. This can be
explained by the point that either the pentavalent intermediate
does not break into ADP‚Pi in the hydrolyzing state or the
pseudorotation of the β-phosphate group is restricted due to
coordination with Mg2+. Both path A and path B studied here
indicates that the pentavalent intermediate is high in energy and
is separated from the reactant and product states with relatively
small barriers. Therefore, we believe that the second explanation
for the Hackney experiments is likely to be correct. Indeed, the
bridging O3β is stabilized by several polar residues including
Asn 233 and Gly 182, while O2β is coordinated to Mg2+; it is
sensible that such a tight coupling with the protein environment
makes the pseudorotation of the β-phosphate group energy
demanding. Potential of mean force calculations associated with
the phosphate pseudorotation will be carried out to obtain more
quantitative understandings. The rotational flexibility of the
γ-phosphate in the ADP‚Pi state also needs to be explored,
because such flexibility is required to explain the rapid exchange
of 18O with the solvent.84-86
Another key goal of the current work is to understand the
atomic details for the regulation of ATP hydrolysis, which is
relevant to the mechanism of mechanochemical coupling in
molecular motors in general.7,8,87 In each functional cycle (e.g.,
myosin in Scheme 1), typically one ATP molecule in solution
binds to the motor protein and is hydrolyzed, followed by the
release of hydrolysis products back into solution. The net free
energy change associated with the entire functional cycle is thus
equivalent to the free energy of ATP hydrolysis in solution
(Scheme 3), which is the free energy that the molecular motor
can harness to generate useful work, although the actual
hydrolysis obviously occurs in the protein. Since energy
dissipation in proteins are on the pico-/nanosecond time scales
without strongly preferred directions,88,89 it is clear that it is
not the free energies of the chemical reactions that are directly
utilized. From this point of view, it is useful for the motor system
to minimize the energy loss as heat. Therefore, an efficient
system would have a very small energetical bias toward the
hydrolysis products even when the system is in the hydrolyzing
state (note especially in the functional cycle of myosin, as shown
in Scheme 1, no work can be done during ATP hydrolysis
because myosin is detached from actin), which is exactly what
has been found experimentally for many motor systems (e.g.,
myosin, F1-ATPase19,90). The computational results here are
also consistent with these considerations. The key to the
mechanochemical coupling, therefore, has to do with the
connection of the protein structure and the ATP molecule in its
various chemical states. Different conformations could be
preferred with different ATP states (solvated ATP, bound ATP,
hydrolysis transition state and ADP + Pi), and free energy is
transferred between ATP and the protein/solvent through
coupled conformational changes of the protein and binding/
chemical modification of ATP. For motors with tracks, such as
myosin and kinesin, interaction with the track also is an
important element. For instance, as shown by the comparison
between the actual processes and imaginary processes where
the myosin-actin interaction is absent (Scheme 3), the binding
energy provided by the actin is the key for an effective functional
cycle; without the binding of actin, the system will get trapped
kinetically in an intermediate state (e.g., M*‚ADP‚Pi).
Using the two high-resolution structures of myosin motor
domains in different kinetic states, we were able to explore the
coupling between the protein conformation and the ATPase
Mechanochemical Coupling in Myosin
J. Phys. Chem. B, Vol. 108, No. 10, 2004 3355
SCHEME 3. Schematic Free Energy for the Myosin-Actin System throughout One Function Cyclea
a
The real processes are connected by solid lines, while imaginary processes are connected with dash-dotted lines; the latter are used to emphaize
the importance of conformational change of the motor domain and the interaction with actin in achieving the mechanochemical coupling.
activity with atomic details. The calculations found high barriers
and a large endothermicity for the ATP hydrolysis in 1FMW,
which are consistent with the suggestion that 1FMW is in the
prehydrolysis kinetic state and therefore is not capable of
catalyzing ATP hydrolysis.40 In the 1VOM structure, by contrast,
the protein is in the conformation that favors ATP hydrolysis;
the QM/MM calculations gave sensible barriers and an exothermicity of -0.4 kcal/mol for path A, which are consistent
with those measured experimentally.19,22 It was found that the
regulation of ATP hydrolysis is largely due to the switch I and
switch II regions in the active site. In the hydrolyzing state
(1VOM), the two regions are stabilized by an important salt
bridge between Arg 238 and Glu 459. This salt bridge is broken
in the prehydrolysis state (1FMW), which has been shown by
the present analysis to have both direct and indirect effects on
the hydrolysis energetics. The direct effect is that, in 1FMW,
Arg 238 and Ser 456 swing closer to the ATP, while Gly 457
and Glu 459 move away from the nucleotide (Figure 4). As a
result, the ATP state is further stabilized and the product state
is less stabilized with the prehydrolysis conformation (1FMW).
However, perhaps more importantly, MD simulations clearly
showed that the break of the salt bridge changes the water
distribution and dynamics in the active site (Figure 5); as a result,
the lytic water molecule is no longer maintained in configurations that favor in-line attacks as in the hydrolyzing conformation (1VOM). These combined effects make the nucleophilic
attack barrier very high in the prehydrolysis state. The critical
role of the salt bridge is consistent with mutation studies,33-35,49,50
which showed that mutating either Arg 238 or Glu 459
decreased the hydrolysis activity substantially, while the double
mutant R238E/E459R is well capable of catalyzing ATP
hydrolysis.
IV. Conclusions
Classical molecular dynamics and combined QM/MM reaction path calculations have been used to explore the catalytic
and regulatory mechanisms of ATP hydrolysis in myosin-II.
These two complementary techniques have yielded useful
insights into different aspects of the hydrolysis cycle, and the
results have general implications for the mechanochemical
coupling in motor proteins in general.
Among the two associative mechanisms studied here, the QM/
MM reaction path calculations with the appropriate hydrolyzing
conformation of the myosin motor domain (PDB code 1VOM)
showed that path A has a lower rate-limiting barrier than path
B; the former involves Ser 236 as the relaying group for the
proton transfer from the lytic water to the γ-phosphate, while
the latter involves a direct proton transfer without relays.
Therefore, it is likely that path A is the preferred mechanism in
wild-type myosin, which is consistent with the fact that Ser 236
is a conserved residue. Perturbation analyses suggested that the
major difference between path A and path B is not due to any
specific protein residues but to the intrinsic difference in the
stereochemistry associated with the two pathways. However,
we also note that if O2γ is protonated in path B (path B2), the
rate-limiting barrier is not much higher than path A. Considering
the limited accuracy of the present QM/MM reaction path
calculations, which have not taken the thermal fluctuations of
the protein into account, it is difficult to exclude the possibility
that path B2 also contributes to the hydrolysis mechanism. As
a matter of fact, this interpretation is qualitatively consistent
with the experimental result that Ser 236A mutant has only
slightly reduced (∼25%) ATP hydrolysis rate.33,35 Despite the
remaining uncertainty in the hydrolysis mechanism, our contribution is having shown that sensible energetics for the
hydrolysis reaction (activation barrier, exothermicity of the
hydrolysis and contribution from active site residues) can be
obtained once the influence from the protein environment is
appropriately taken into account; the much higher barrier found
in previous work is most likely due to the neglect of the protein
environment in the calculations.78
A particularly encouraging result is that QM/MM calculations
correctly reproduced the trend that ATP hydrolysis has much
higher barrier and endothermicity with the prehydrolysis
conformation of the motor domain (PDB structure 1FMW),
which is consistent with the notion that the prehydrolysis
conformation is not capable of catalyzing ATP hydrolysis. The
current analysis indicated that the conformational regulation of
3356 J. Phys. Chem. B, Vol. 108, No. 10, 2004
ATP hydrolysis in myosin is largely determined by several
residues in the switch I and switch II regions. In particular, the
salt bridge between Arg 238 and Glu 459, which is broken in
1FMW, was shown to have both direct and indirect effects. The
Arg 238 is closer to ATP in 1FMW than in 1VOM, which makes
the ATP state more stabilized than the hydrolysis products
(ADP‚Pi). Furthermore, classical MD simulations clearly showed
that water structures in the active site are different in the two
motor conformations. In 1VOM, the salt bridge between Arg
238 and Glu 459 helps to stabilize the water structure in which
the lytic water has nearly perfect in-line attack conformation.
In 1FMW, by contrast, the salt bridge is broken, and therefore,
water molecules undergo large fluctuations and on average do
not have the appropriate position for in-line attacks, which also
makes the hydrolysis reaction highly unfavorable.
The current work represents our initial efforts to understand
the atomic details of mechanochemical coupling in molecular
motors. Further studies are required to generate a more complete
understanding and to confirm the current analysis. For example,
there are still other possible mechanisms for the hydrolysis, such
as the dissociative pathway. Although previous theoretical
studies by Warshel and co-workers found that dissociative and
associative pathways are close in energies in Ras p21,91-93 the
structure of the ADP‚vanadate structure suggests that the
associative pathway is very likely; this certainly cannot exclude
the dissociative pathway. Although γ-phosphate being the
general base for its hydrolysis seems widely accepted in the
myosin field since there is no general base within 5 Å, the issue
remains controversial in the general area of phosphate hydrolysis
and one might indeed envision other pathways for generating a
nucleophilic OH- group. For example, it has been suggested
that Glu 459 may act as the general base through the hydrogenbond network involving water molecules.50 Finally, a recent
Car-Parrinello simulation found that Lys 185 protonates the
γ-phosphate in a spontaneous fashion within 150 fs of MD,
which led the authors to the suggestion that Lys 185 can act as
the general acid that catalyzes the hydrolysis;48 it has been
commented that,14 however, the observed proton transfer might
be an artifact due to the small number of protein residues
explicitly included in that simulation. The present study has not
addressed these possibilities, because these mechanisms involve
more significant perturbations to the active site structure, and
therefore a reaction path QM/MM study is not sufficient. Also
not explored are other possible protonation patterns associated
with ATP, ADP/Pi, and the ligands of the Mg2+ ion; e.g., given
the pKa’s sufficiently close to 7, ATP might be protonated, and
one of the ligands (Thr 185, Ser 237) might be deprotonated.
Model studies of monophosphate hydrolysis found that the
energetics of associative pathway are rather similar for monoanionic and doubly anionic phosphates.47 All these issues need
to be explored in more details in the future using SCC-DFTB/
CHARMM,75 which is sufficiently fast and allows adequate
conformational samplings.94 In terms of the conformational
regulation of ATP hydrolysis, a free energy perturbation study
has been carried out to complement the QM/MM reaction path
analysis; the overall trends were very consistent in the two
studies. Finally, much more studies are required to understand
the mechanisms of conformational transitions in the motor
domains and, perhaps more importantly, the effect of myosinactin interaction on the binding properties of ATP, ADP, and
Pi.
As a final note, it is interesting to consider the mechanochemical coupling in molecular motors as a special case of
“dynamical disorder” in catalysis.95 Elegant single molecule
Li and Cui
studies have revealed that many enzymes have slow fluctuations
in their conformations that modulate the kinetics of the chemical
reaction being catalyzed.96-98 Structural details for such slow
fluctuations, in most cases, however, remain to be elucidated.
Molecular motors are great systems to explore dynamical
disorders because structural fluctuations have a major impact
on the chemistry and is a key characteristic of the system (in
contrast to, for example, cholesterol oxidase,96 where the
variation in rate was found to be less than a factor of 10), which
might make it easier to analyze the identity of the slow
fluctuations.
Acknowledgment. The Q.C. group is partially supported by
the starting-up fund from the Department of Chemistry and
College of Letters and Science at University of Wisconsin,
Madison, a PRF-G grant from the donors of the Petroleum
Research Fund, administered by the American Chemical Society,
and a Research Innovation Award from the Research Corp. We
thank Prof. I. Rayment, S. Gilbert and D. Hackney for discussions and encouragements.
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